There are 9 Halo 2 playlists in total to complete. For this achievement you only need to do 3 of them.
The two easiest ones to complete are the Boss Fights (3 missions) and the Fan Favorites (4 missions). If you're quick, you can probably finish these both in under 2 hours.
By doing this you will also unlock the achievement Seconds
The third playlist that should be completed is either the Arbiter's Journey (7 missions) or one of the 4 campaign playlists (15 missions). I suggest doing the campaign playlist because the achievements for the campaign playlist also count towards the campaign achievement list. Also the skulls, terminals and other collectables can all be found in the playlist campaign as well.
But if you're like me and didn't know about the playlist overlap with the campaign, the Arbiter's Journey will take significantly less time to complete than doing the campaign all over again.
Some people have noted for the playlist based achievements that sometimes you need to complete 4 playlists in order to unlock any of the "complete three Halo playlists" achievements. So if this achievement doesn't unlock for you after you are returned to the MCC main menus then you will likely need to complete a 4th playlist.